Anomaly free cosmological perturbations with generalised holonomy correction in loop quantum cosmology

Abstract

In the spatially flat case of loop quantum cosmology, the connection is usually replaced by the holonomy in effective theory. In this paper, instead of the standard scheme, we use a generalised, undetermined function to represent the holonomy and by using the approach of anomaly free constraint algebra we fix all the counter terms in the constraints and find the restriction in the form of , then we derive the gauge-invariant equations of motion of the scalar, tensor and vector perturbations and study the inflationary power spectra with generalised holonomy correction.